Experimental investigation on flow boiling heat transfer in conventional and mini vertical channels

International Journal of Heat and Mass Transfer 107 (2017) 225–243

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Experimental investigation on flow boiling heat transfer in conventional and mini vertical channels Qi Lu, Deqi Chen ⇑, Chong Li, Xueqiang He Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing 400044, China

a r t i c l e

i n f o

Article history: Received 13 July 2016 Accepted 7 November 2016 Available online 19 November 2016 Keywords: Flow boiling Heat transfer Bubble behavior Forced convection with evaporation

a b s t r a c t An experimental investigation was carried out to study the flow boiling heat transfer mechanism in the vertical channels with different inner diameters. The heating section of the test-section was stainless steel tube, and the transparent sections were equipped at inlet and outlet of the test-section, respectively. The flow patterns at outlet were recorded by a high speed camera, and the corresponding experimental parameters were measured simultaneously. In this study, the characteristics of flow boiling heat transfer with different inner diameters, inlet water temperatures, mass fluxes, and heat fluxes were analyzed in detail. Moreover, a modified correlation on the Chen correlation was proposed to predict the heat transfer coefficients in the vertical channels, and this correlation was verified with good agreement. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Flow boiling heat transfer systems are widely used in industries, such as aerospace, electronics, and chemistry. Due to the effective heat removal and maintenance of relatively uniform surface temperatures during the heat transfer process, the flow boiling heat transfer in mini scale channels has received much attention. Over the years, there has been much debate about what identifies a channel size as conventional or mini since the heat transfer and flow characteristics can be different over the ranges of millimeter to sub-millimeter size. A critical diameter of 3 mm was suggested by Kandlikar [1] for the conventional-to-mini channel threshold. A threshold of 6 mm for conventional-to-mini scale channel was proposed by Mehendal et al. [2]. Meanwhile, Chen et al. [3] proposed that the channels with the diameters of 1.10 mm and 2.01 mm exhibited strong ‘‘mini channel characteristics”. However, Ribatski et al. [4] suggested that these criterions adopted here did not take into account differences in the twophase flows and heat transfer processes in conventional and mini scale channels. Kew and Cornwell [5] proposed an approximate physical criterion for conventional-to-mini scale channel threshold diameter based on the confinement of a growing bubble within a channel as follows:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Nconf ¼

r

gðql  qg ÞD2in

⇑ Corresponding author. E-mail address: [email protected] (D. Chen). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.11.020 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

ð1Þ

where Nconf is the confinement number; r is the surface tension (N/ m); g is the acceleration of gravity (m2/s); Din is the inner diameter (mm); ql is the density of liquid phase (kg/m3), and qg is the density of vapor phase (kg/m3). As mentioned by Kew and Cornwell [5], the critical Nconf for conventional-to-mini scale channel is about 0.5, therefore the critical diameter between conventional and mini scale channel is about 5 mm for saturated water (0.101 MPa). Widely accepted is that two mechanisms are considered to dominate flow boiling heat transfer: the nucleate boiling and the forced convection with evaporation. As described by Charnay et al. [6], the nucleate boiling was dependent on the heat flux and the saturation pressure. However, the forced convection with evaporation was related to the conduction and convection through the liquid film, which was dependent on the mass flux and the vapor quality. As proposed by Tran et al. [7], the boundary between the nucleate boiling and the forced convection with evaporation was a function of the wall superheat. The nucleate boiling region occurred at high wall superheat, while the forced convection with evaporation region occurred at low wall superheat. These mechanisms could coexist with vapor quality as suggested by Vlasie et al. [8] and Collier and Thome [9], where the heat transfer coefficient depended on heat flux, mass flux and vapor quality. Generally, these boiling mechanisms were usually assumed to be independent of each other due to the simplicity of discussion about flow boiling heat transfer. Some authors (Tran et al. [7], Bao et al. [10] and Ali et al. [11]) suggested that the major trend of flow boiling heat transfer in mini-channel was that the heat transfer coefficients were only a function of heat flux, and largely independent on vapor quality or mass flux, which indicated that the nucleate boil-

226

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

Nomenclature

General symbol the confinement number Nconf the inner diameter (mm) Din G the mass flux (kg/m2 s) T the temperature (°C) q the density (kg/m3) U the voltage (U) I the current (A) Q the power (kW) q the heat flux (kW/m2) / the power density (W/m3) C the perimeter of the inner cross section (m) L the length of the heating section (m) r the radius (m) A the area of the inner cross section (m) z the distance (m) a the constant k the thermal conductivity (W/m K) h the heat transfer coefficient (kW/m2 K) xe the equilibrium quality H the enthalpy (J/kg) Hfg the latent heat of vaporization (J/kg) DTsat the wall superheat (K), Tw  Tsat DPsat the difference in vapor pressure corresponding to DTsat (kPa) P the pressure (kPa) Re the Reynolds number Pr the Prandtl number

ing mechanism dominated in mini-channel. In addition, Huo et al. [12] experimentally investigated the boiling heat transfer in vertical mini-channels with R134a as the working fluid. It was found that the dominant characteristics of the heat transfer was the nucleate boiling as the vapor quality was less than 20%–30% with the channel diameter of 2.01 mm and 40%–50% with the channel diameter of 4.26 mm. However, Lin et al. [13] demonstrated that both mechanisms of the nucleate boiling and the forced convection with evaporation occurred in mini-channels. All the works mentioned above used hydrocarbon fluids, which were much different from water in physical properties such as the boiling point and the latent heat of vaporization. The research conducted by Qu and Mudawar [14] and Bang et al. [15] proposed that the heat transfer coefficient generally presented a positive relationship with the mass flux and the vapor quality in the case of water used for the working fluid, which indicated that the forced convection with evaporation dominated attributed to the considerable vaporization latent heat of water. Also, Karayiannis et al. [16] suggested a progression from the nucleate boiling to the forced convection with evaporation as the heating length increased. Sumith et al. [17] carried out an experiment to research the flow boiling heat transfer in a vertical channel with inner diameter of 1.45 mm. It was concluded that the heat transfer mechanism deviated from the nucleate boiling and closely resembled the forced convection with evaporation as flow pattern transferred to annular flow. Also, it was possible for nucleate boiling to continue even in the liquid film of the wavy-annular flow as the liquid film was thick enough. As is known to all, the region of two-phase flow initiates at the onset of nucleate boiling (ONB) where nucleation requires a high degree of the wall superheat. As proposed by Piasecka and Poniewski [18], a considerable rise above the saturation point of

cp F S Xtt Bo M

the the the the the the

specific heat (J/kg K) enhancement factor suppression factor Martinelli parameter boiling number molecular weigh

Greek letters r the surface tension (N/m) l the dynamic viscous (Pas) g the acceleration of gravity(m2/s) Subscripts tot total w/wall wall in inner m mixture sat saturated v vapor phase l liquid phase tp two-phase b bulk cr critical fc forced convection pb pool boiling exp experimental value pre predicted value

wall temperature could occur before boiling with certain conditions. This temperature overshoot, also known as ‘‘superheated excursion” and ‘‘nucleation hysteresis” was conspicuous as for highly wetting dielectric fluids (e.g., refrigerants). Lie and Lin [19] found that a significant wall temperature overshoot of about 20 K at ONB was found for R134a in a horizontal narrow annular duct. However, the wall temperature overshoot was just 3 K at ONB with the cyclohexane as the working fluid as proposed by Liu and Bi [20]. The effect of hydraulic diameter on the heat transfer coefficient is somewhat inconsistent in published literatures. Owhaib et al. [21] suggested that the reduction of the hydraulic diameter (circular channel) caused the heat transfer coefficients to increase. Saitoh et al. [22] studied the boiling flow in three channels with diameters of 0.51 mm, 1.12 mm, 3.1 mm, respectively. The results showed that the maximum heat flux increased with the hydraulic diameter reducing. Also, the maximum heat flux occurred for lower quality as the hydraulic diameter reducing. Additionally, Sobierska et al. [23] proposed that the reduction of the hydraulic diameter strongly enhanced the influence of the vapor quality on the heat transfer coefficient. In contrast, Dupont and Thome [24] showed that the heat transfer coefficient decreased with hydraulic diameter increasing from 0.5 mm to 2 mm as x > 0.18. In general, it is crucial to distinguish the stable boiling during flow boiling heat transfer experiments, but there is not a theoretical criteria to distinguish them. Consolini and Thome et al. [25] indicated that the heat transfer coefficient for stable boiling gradually increased with the vapor quality up to a high value whilst it did not change obviously. As mentioned by Karayiannis et al. [16], the local wall temperature and heat transfer coefficient could highly fluctuate for unstable boiling. Moreover, the liquid film

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

might be ruptured due to high Kelvin-Helmholtz instability and the dry out might occur at low vapor quality. Also, Ohta et al. [26] investigated the effect of the flow fluctuation at the test section inlet on flow boiling heat transfer. It was concluded that the boiling heat transfer characteristics in mini-channels could be changed significantly by altering flow fluctuation from rapid axial growth of elongated bubbles at low vapor quality. Additionally, the regulation of inlet flow rate seemed to be a key parameter in reducing the scattering of heat transfer data encountered in flow boiling of mini-channels. Brutin et al. [27] suggested that vapor slugs blocked two-phase flow containing it to the entrance, creating back-flow, which caused the unsteady behavior. While many studies focused on flow boiling heat transfer, the fundamental reasons for the flow boiling heat transfer mechanisms between conventional and mini channels have not been clearly explained, especially with correspondent bubble behavior evolutions and flow parameter characteristics. The subject of this study is to investigate the flow boiling heat transfer mechanisms between conventional and mini channels with different working conditions. Moreover, a modified correlation based on the Chen [28] correlation is proposed in this study by considering the effects of channel confinement (Nconf), vapor generation (Bo), and interaction between two phases (Xtt). A good agreement is achieved between the predicted results and experimental results.

2. Experimental apparatus The schematic diagrams of the experimental loop system and the test-section are shown in Fig. 1a and Fig. 1b, respectively. The heating section of test-section is made of 304 stainless steel seamless cold drawn tube with the inner diameters of 2.15 mm, 4.99 mm and 6.88 mm, respectively. The heating section lengths are 300 mm, and the wall thicknesses are 0.93 mm (Din = 2.15 mm), 0.51 mm (Din = 4.99 mm) and 0.57 mm (Din = 6.88 mm). As shown in Fig. 1b, the transparent sections equipped at the inlet and outlet of the test-section are made of Polycarbonate with the length of 100 mm. The inner diameter of the transparent section is the same as that of the heating section. Seven T-type thermocouples with the diameter of 0.2 mm are uniformly placed along the heating section. Two T-type thermocouples are equipped at the inlet and outlet of the test-section to measure the water temperature. The pressures at the inlet and outlet of the test section are measured by two differential pressure transducers (YOKOGAWAEJA110A). The test-section is heated by a D.C. power unit (Uout = 0 V  12 V, Iout = 0 A  2 KA). Also, the uncertainties of the voltage and the current are 0.0043% and 0.2%, respectively. In this experimental study, the deionized water is used as the working fluid. Experiments are carried out with different working conditions, including different inner diameters, different inlet water temperatures, different liquid mass fluxes and heat fluxes. All the working conditions are summarized in Table 1. The experimental study is carried out under atmosphere (0.101 MPa) and the environmental temperature (30 °C). As for the experimental set-up, the working fluid is pump driven to flow through an orifice meter, and the uncertainty of the orifice meter is less than 0.1% after calibration. The driving pressure head generated by the pump is adjusted to keep a constant time-averaged mass flux of the working fluid during the experimental study. Before the working fluid flowing into the test-section, it is preheated by a cartridge heater to raise the fluid temperature to the desired temperature. The uncertainties of temperature measurement and pressure measurement are less than 0.5 K and 0.067%, respectively. All the measured parameters, including liquid mass flux, temperature, DC current, DC voltage and pressure are recorded by an Agilent acquisition system. During

227

this experimental study, the flow patterns at outlet are captured by a high speed camera (Redlake-HG-100 K) with a micro-lens, and the recording speed is 5000 fps (frame per second) with an LED light used for illumination. In this study, the micro-lens of the high speed camera is equipped in front of the transparent section of outlet normal to the flow direction to avoid the shadow interference and light refraction, as shown in Fig. 1a. 3. Data reduction and stability criteria 3.1. Data reduction The imposed heat flux for the fluid flowing through the circular channel is calculated based on the total power input,

Q tot ¼ UI

ð2Þ

where Qtot is the total input power (W); U is the voltage (V) and I (A) is the current. Therefore, the heat flux can be obtained as follows,

q ¼ ðQ tot  Q loss Þ=CL

ð3Þ

where q is the heat flux (kW/m2); Qloss is the heat loss (W) with the value of 3% of total input power; C is the perimeter of the inner cross section (m) and L is the length of the heating section (m). Moreover, the heat conduction of the circular channel in the cylindrical coordinate is shown in Fig. 1b, and the partial differential heat conduction equation can be defined as follows,

  1 @ @T w _ ¼0 þU kw r c rc @r c @r c

ð4Þ

where rc is the radius of the channel (m); kw is the thermal conductivity of the heating wall (W/m K); Tw is the temperature of the heating wall (°C) and / is the power density (W/m3). Also, the conditions for unique solution to Eq. (4) can be expressed as follows,

The inner wall temperature can be expressed as follows,

T w;in ¼ 

U 4kw

r 2c;in þ a1 ln r c;in þ a2

ð7Þ

Thus, the heat transfer coefficient can be defined as follows,

hw7 ¼

q T w7;in  T m7

ð10Þ

where hw7 is the heat transfer coefficient at No. 7 (kW/m2 K); Tw7,in is the inner wall temperature at No. 7 (°C); Tm7 is the mixture temperature of water and vapor at No. 7 (°C). Additionally, the thermal equilibrium vapor quality can be calculated by the following equation,

xe7 ¼

Hm7  Hsat Hfg

ð11Þ

228

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

Atmosphere

Heat Exchanger Liquid Tank 1

Liquid Tank 2

dp

p

T

Camera

Test section

High Speed

Pump

Preheater T Orifice Flowmeter P

Valve

P Pressure

T Temperature

Experimental apparatus

100 mm

Aluminum Foil T-type Thermocouple

Transparent Section

Stainless Steel Channel

Toutlet

Glass Fibres Water

Pout

-

50 mm

T7

T-type Thermocouple Kapton Scotch

50 mm

T6

50 mm

T5

50 mm

T4

Din

Heating Section

50 mm

T3

50 mm

T2

T1

+ Pin

100 mm

Tinlet Transparent Section

Test-section Fig. 1. The schematic diagram of experiment.

229

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243 Table 1 Working conditions. Din (mm)

Tinlet (°C)

Gl (kg/m2 s)

q (kW/m2)

DPmean (kPa)

xeONB

xeFDB

Number

2.15

70

700 1000 700 1000 1500 700 1000 1500

50–210 50–220 50–200 50–220 50–330 50–190 50–220 50–230

14.69 15.93 15.09 16.88 31.14 16.14 20.16 23.77

0.0078 0.0122 0.0129 0.0099 0.0071 0.0103 0.0082 0.0074

0.0078 0.0122 0.0129 0.0099 0.0071 0.0103 0.0082 0.0074

17 18 16 18 14 15 18 12

300 400 500 600 700 300 400 500 600 700

140–230 260–320 300–360 380–440 440–500 70–140 80–150 80–160 100–180 130–200

7.024 8.288 8.496 8.72 8.992 8.512 8.672 8.88 9.056 9.232

0.0387 0.0368 0.0364 0.0371 0.0363 n 0.0161 0.0182 0.0187 0.0146

0.0339 0.0342 0.0332 0.0348 0.0346 0.0076 0.0038 0.0055 0.0073 0.0074

5 4 4 5 4 8 8 8 9 8

300 400 500 600 700 300 400 500 600 700

50–220 50–240 50–250 50–240 50–260 50–190 50–190 50–200 50–230 50–270

6.27 6.37 6.58 7.14 7.80 6.52 6.69 6.97 7.30 7.88

0.0313 0.0322 0.0294 0.0314 0.0310 0.0185 0.0192 0.0203 0.0200 0.0198

0.0204 0.0222 0.0208 n n 0.0034 0.0092 0.0085 0.0073 0.0059

18 20 21 20 22 14 15 15 19 22

75

80

4.99

70

80

6.88

70

80

Total

377

Hm7 ¼ Hinlet þ

qCz7 Gl A

ð12Þ

120

0.03

110

0.01

100

-0.01

In order to distinguish the stable boiling and the quasi-stable boiling, experiments were carried out to show these boiling phenomena. The stable state was defined by the criteria proposed by Karayiannis et al. [16], i.e. the fluctuation amplitudes of all the parameters were less than 5% including the pressure drop, the mass flux, and the wall temperature at No. 7. Additionally, an example of stable boiling in the specific working condition is shown in Fig. 3a (Din = 2.15 mm, Tinlet = 80 °C, Gl = 700 kg/m2 s, q = 50 kW/m2). As for quasi-stable boiling, the mass flux and wall temperature at No. 7 remain stable, while the pressure drop presents obvious fluctuation (DPin > 5%) with mean value constant. Fig. 3b illustrates the case for quasi-stable boiling in the specific working condition (Din = 2.15 mm, Tinlet = 80 °C, Gl = 700 kg/m2 s, q = 110 kW/m2). As shown in Fig. 3b, the pressure drop appears significant fluctuation of 13.07%, but the mass flux and the wall temperature at No. 7 keep stable state. Also, the period of pressure drop is about 95 s. All the data as mentioned above are recorded for 180 s, which is much longer than one cycle of pressure fluctuation. Moreover, time-averaged values have been evaluated as arithmetic mean values of all measured data in this recording period.

xe

Twall (°C)

where xe7 is the thermal equilibrium vapor quality at No. 7; Hm7 is the mixing enthalpy of vapor and water at No. 7 (J/kg); Hsat is the saturated water enthalpy (J/kg); Hfg is the latent heat of vaporization (J/kg); Hinlet is the water enthalpy at inlet of the heating section (J/kg); Gl is the mass flux (kg/m2 s); z7 is the distance from the inlet of the heating section to No. 7 (m), and A is the area of the inner cross section (m2). Meanwhile, Fig. 2 shows the variation of wall temperature along the channel from inlet to outlet and the axial cross-sectional average quality variation along the channel with the specific working condition (Din = 2.15 mm, Tinlet = 70 °C, Gl = 700 kg/m2 s, q = 150 kW/m2).

3.2. Stability criteria

4. Results and discussion 90

-0.03 Twall xe

80

-0.05 1

2

3

4 Location

5

6

7

Fig. 2. the variation of wall temperature and the axial cross-sectional average quality variation along the channel with the specific working condition (Din = 2.15 mm, Tinlet = 70 °C, Gl = 700 kg/m2 s, q = 150 kW/m2).

4.1. Flow boiling heat transfer characteristics in conventional-channel (Din = 6.88 mm) The following section includes analysis on the flow boiling heat transfer characteristics in the circular channel with inner diameter of 6.88 mm for different working conditions. Firstly, the flow boiling heat transfer characteristics with the inlet water temperature of 80 °C for different mass fluxes are analyzed in detail. As for the specific working condition (Din = 6.88 mm, Tinlet = 80 °C), the

230

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

8

12

Δ P(kPa)

14

Δ P(kPa)

10

ΔPmean=7.67 kPa, Δ(ΔP)=1.11%

6

ΔPmean=8.86 kPa, Δ(ΔP)=13.07%

10

8

4

6

2 0

45

90 t (s)

135

0

180

45

720

720

710

710

Gl (kg/m2s)

Gl (kg/m2s)

135

180

(1) Τhe fluctuation of pressure drop

(1) The fluctuation of pressure drop

Gl, mean =695.62 kg/m 2s, ΔGl=0.84%

700

90 t (s)

Gl, mean=706.93 kg/m2s, ΔGl=0.34%

700

690

690

680

680 0

45

90 t (s)

135

180

0

(2) The fluctuation of mass flux

45

90 t (s)

135

180

(2) The fluctuation of mass flux 135

135

125

Twall, 7 (°C)

Twall, 7 (°C)

125

Twall, 7, mean=100.89 °C, ΔTwall, 7=0.42%

115

115 Twall, 7, mean=108.01 °C, ΔTwall, 7=1.15%

105

105

95

95 0

45

90 t (s)

135

180

(3) The fluctuation of wall temperature

a

0

45

90 t (s)

135

180

(3) The fluctuation of wall temperature

b

Fig. 3. The variation of experimental parameters with time (Din = 2.15 mm, Tinlet = 80 °C, Gl = 700 kg/m2 s, a: the stable boiling state with q = 50 kW/m2; b: the quasi-stable boiling state with q = 110 kW/m2).

variation of heat transfer coefficient with equilibrium quality for different mass fluxes is illustrated in Fig. 4a. In the research of Tong and Tang [29], it was suggested that the wall temperature started to decrease or bend at the onset of nucleate boiling (ONB), which was decided by working conditions. In addition, the wall temperature followed a curve of partial boiling and then reached an

approximately constant value at the fully developed boiling (FDB). As for the boiling curve, the onset of nucleate boiling (ONB) was defined at the initiation of heat flux bending, and the fully developed boiling (FDB) was defined at the end of heat flux bending. As shown in Fig. 4a, the two-phase flow starts at negative equilibrium quality for all considered mass fluxes. Also, the

231

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

16

16 FDB (Gl300-Gl700)

8

12 hwall, 7 (kW/m2K)

hwall, 7 (kW/m2K)

12

ONB (Gl300-Gl700)

Gl300 Gl400

4

8

ONB (Gl300-Gl700)

Gl300 Gl400 Gl500

4

Gl500 Gl600

FDB (Gl300-Gl500)

Gl600 Gl700

Gl700

0 -0.05

-0.03

-0.01 xe7

0.01

0 -0.05

0.03

-0.03

(1) hwall, 7-xe7

-0.01 xe7

0.01

0.03

(1) hwall, 7-xe7

30

30

20

15 Twall, 7-Tsat (°C)

Twall, 7-Tsat (°C)

ONB (Gl300-Gl700)

ONB (Gl300-Gl700)

10 FDB (Gl300-Gl700)

Gl300 Gl400

0

FDB (Gl300-Gl500)

0 Gl300 Gl400

-15

Gl500 Gl600

Gl500 Gl600

Gl700

Gl700

-10 -0.05

-0.03

-0.01 xe7

0.01

-30 -0.05

0.03

(2) (Twall, 7-Tsat, 7)-xe7

-0.03

-0.01 xe7

0.01

0.03

(2) (Twall, 7-Tsat, 7)-xe7

300

300 FDB (Gl600-Gl700) FDB

FDB (Gl300-Gl500)

225

225

(Gl500)

150

q (kW/m2)

q (kW/m2)

ONB (Gl700)

ONB (Gl300-Gl700)

Gl300 Gl400

75

Gl500 Gl600 Gl700

0 -10

0

10 Twall, 7-Tsat (°C)

20

30

ONB (Gl500-Gl600)

FDB(Gl400)

150

FDB(Gl300)

Gl300 Gl400

75 ONB (Gl300-Gl400)

0 -30

-15

0 Twall, 7-Tsat (°C)

15

(3) q-(Twall, 7-Tsat, 7)

(3) q-(Twall, 7-Tsat, 7)

a

b

Gl500 Gl600 Gl700

30

Fig. 4. The flow boiling with different mass fluxes (a: Din = 6.88 mm, Tinlet = 80 °C°C; b: Din = 6.88 mm, Tinlet = 70 °C).

discrepancy between equilibrium quality at ONB with different mass fluxes is not obvious. Also, the equilibrium quality of FDB does not present obvious regularity for considered mass fluxes.

As shown in Fig. 4a, the heat transfer coefficient increases with equilibrium quality for different mass fluxes since the heat flux increases, but the trends of these variation are different. As for

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

16 High Subcooled Region

Single Phase Region

Low Subcooled Region

Fo

rc e

dC

Saturated Region n t io o ra ap Ev ith w n ti o vec on

FDB (quasi-stable boiling)

4

Su b

ONB

led

Nu

cle

ate

Bo

ili ng

8

co o

hwall, 7 (kW/m 2K)

12

Forced Convection

0 -0.05

-0.03 (-0.0185)-0.01 (-0.0034) 0.01 xe7

0.03

(1) hwall, 7-xe7 160

30 Single Phase Region

High Subcooled Region

Saturated Region

15

130

0

100

ONB

-15

FDB (quasi-stable boiling)

Twater (°C)

Low Subcooled Region

Twall, 7-Tsat (°C)

low equilibrium quality (xe < xeONB), the dominant heat transfer mechanism is the forced convection. As the equilibrium quality increases (xe > xeONB), the flow boiling gradually enhances and the heat transfer coefficient linearly increases with equilibrium quality due to the nucleate boiling. As for xe > xeFDB, the discrepancy between the heat transfer coefficient for different mass fluxes is significant. Moreover, the heat transfer coefficient increases with increasing the mass flux. The flow boiling mechanism includes the nucleate boiling and the forced convection with evaporation, but the proportion of each mechanism with the equilibrium quality need to be researched more carefully in future study. As the inlet water temperature decreases to 70 °C, the variation of heat transfer coefficient and wall superheat with equilibrium quality for different mass fluxes, and the boiling curves for different mass fluxes are illustrated in Fig. 4b. As shown in Fig. 4b, it is obvious that the effect of mass flux on ONB is not significant, which is the same as that with Tinlet = 80 °C. However, the equilibrium quality at ONB with Tinlet = 70 °C is significantly smaller than that with Tinlet = 80 °C. The corresponding equilibrium quality at FDB with Tinlet = 70 °C is also smaller than that with Tinlet = 80 °C. Moreover, FDB does not appear for Gl = 600, 700 kg/m2 s due to heat flux not large enough. To explain the effect of equilibrium quality on the heat transfer coefficient more reasonably, it is necessary to discuss these phenomena with the coinciding flow patterns. As for the specific working condition (Din = 6.88 mm, Tinlet = 80 °C, Gl = 300 kg/m2 s), the variation of heat transfer coefficient with equilibrium quality, the variation of wall superheat and water temperature with equilibrium quality, and the boiling curve are illustrated in Fig. 5. It can be clearly seen that the equilibrium quality covers the single phase region to the saturated region. According to analysis on the variation of heat transfer coefficient, three types of heat transfer mechanisms are distinguished, including the forced convection, the nucleate boiling and the forced convection with evaporation. As the equilibrium quality gradually increases to that of ONB (xeONB = 0.0185), the flow pattern transfers from the single phase to the isolated bubbly flow, as shown in Fig. 6a. As for xeONB = 0.0185, the dominant heat transfer mechanism is the nucleate boiling, which is significantly affected by the heat flux, namely the equilibrium quality. The numbers of bubbles generating at the nucleation sites are much small, and the bubble growth rates are low due to low heat flux (q = 60 kW/m2). The highly subcooled boiling region (0.0185 < xe < 0.0034), the heat transfer coefficient linearly increases with the equilibrium quality, hence the dominant heat transfer mechanism of the nucleate boiling remains unchanged. As the equilibrium quality increases to 0.0034 (xeFDB = 0.0034), the flow pattern starts to present typical churn flow with obvious turbulence between the liquid-vapor interface, as shown in Fig. 6b. Also, the flow boiling starts to appear quasi-stable boiling state, as shown in Fig. 7. As the equilibrium quality increases to 0, the flow boiling accesses the saturated boiling region. Obviously, the flow pattern presents the typical annular flow in this region, as shown in Fig. 6c. The vapor core flows quickly in the center of the channel with liquid droplets entrained, and the liquid film surrounding the vapor core flows fast along the heating wall. Therefore, the dominant heat transfer mechanism is the forced convection with evaporation. The fast flowing liquid film takes away much heat from the heating wall, and then the heat is transferred to the liquid-vapor interface through the conduction of liquid film, finally the heat is transferred to the vapor core contributing to the evaporation of liquid film on the liquidvapor interface. As for the forced convection with evaporation, the heat transfer coefficient is mainly affected by the mass flux and not significantly related to the heat flux, hence the heat transfer coefficient does not change obviously with increasing the equilibrium quality, as shown in Fig. 5.

70 Twall, 7-Tsat Twater

-30 -0.05

-0.03 (-0.0185) -0.01(-0.0034) 0.01

40 0.03

xe7

(2) (Twall, 7-Tsat, 7)-xe7 300

225

q (kW/m2)

232

150

FDB (quasi-stable boiling)

75

0 -10

ONB

0

10 Twall, 7-Tsat (°C)

20

30

(3) q-(Twall, 7-Tsat, 7) Fig. 5. The flow boiling (Din = 6.88 mm, Tinlet = 80 °C,Gl = 300 kg/m2 s).

As the inlet water temperature decreases to 70 °C, the flow boiling presents different characteristics as compared to Tinlet = 80 °C. As shown in Fig. 8, the equilibrium qualities at ONB (xeONB = 0.0313) and FDB (xeFDB = 0.0204) for 70 °C are less than those for 80 °C (xeONB = 0.0185, xeFDB = 0.0034). As shown in Fig. 9a and b, the corresponding flow patterns are the isolated bubbly flow and the slug flow, respectively. Additionally, the dominant

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

233

and the flow pattern presents typical annular flow, as shown in Fig. 9d. Meanwhile, the dominant heat transfer mechanism transfers from the nucleate boiling to the forced convection with evaporation. With increasing the equilibrium quality, the liquid film of annular flow significantly decreases. As the equilibrium quality increases to 0.0086, the evaporation of liquid film on the liquidvapor interface is so intense that the liquid film sometimes breaks, namely the boiling crisis. Additionally, the heat transfer coefficient rapidly decreases and the wall superheat quickly increases after the boiling crisis, as shown in Fig. 8. 4.2. The flow boiling heat transfer characteristics in mini-channel (Din = 2.15 mm)

a xe=-0.0185 Isolated Bubbly Flow

b

c

xe=-0.0034

xe=0.0006

Churn Flow

Annular Flow

Fig. 6. The flow patterns with different equilibrium qualities (Din = 6.88 mm, Tinlet = 80 °C, Gl = 300 kg/m2 s).

heat transfer mechanism of nucleate boiling remains unchanged between ONB (xeONB = 0.0313) to FDB (xeFDB = 0.0204). As for FDB with Tinlet = 70 °C and Tinlet = 80 °C, the corresponding heat fluxes are almost the same, namely, 120.04 kW/m2 and 121.04 kW/m2, respectively. Moreover, the difference between wall superheats with Tinlet = 70 °C and Tinlet = 80 °C is also mild, namely, 13.92 K and 12.78 K, respectively. Therefore, the equilibrium quality with Tinlet = 80 °C (xeFDB = 0.0034) is larger than that with Tinlet = 70 °C (xeFDB = 0.0204), and the flow pattern transfers from the churn flow to the slug flow with the inlet water temperature decreasing from 80 °C to 70 °C. Meanwhile, the churn flow is a typical flow pattern with obvious fluctuations of experimental parameters (DP), hence FDB and quasi-stable boiling simultaneously appear for Tinlet = 80 °C. In addition, the flow pattern transfers from the slug flow to the churn flow with the equilibrium quality increasing from xeFDB = 0.0204 to xe = 0.0075 of quasi-stable boiling for Tinlet = 70 °C, as shown in Fig. 9c. As shown in Fig. 10, the pressure drop presents obvious fluctuations for Tinlet = 70 °C. The discrepancy between periods of the pressure drop for Tinlet = 70 °C and Tinlet = 80 °C is mild, but the amplitudes are much different. It is clear that the amplitude of pressure drop for Tinlet = 70 °C (D(DP) = 15.08%) is significantly larger than that for Tinlet = 80 °C (D(DP) = 9.25%). As the equilibrium quality increases above 0, the flow boiling accesses the saturated boiling region,

To investigate the flow boiling phenomena in the mini-channel, the experiments are carried out in a circular channel with the inner diameter of 2.15 mm. The effects of the heat flux, mass flux and inlet water temperature on the flow boiling heat transfer are discussed in detail. As for the specific working condition (Din = 2.15 mm, Tinlet = 80 °C), the variation of heat transfer coefficient and wall superheat with equilibrium quality for different mass fluxes (Gl = 700 kg/m2 s, Gl = 1000 kg/m2 s, Gl = 1500 kg/m2 s), and the boiling curves for different mass fluxes (Gl = 700 kg/m2 s, Gl = 1000 kg/m2 s, Gl = 1500 kg/m2 s) are illustrated in Fig. 11. It can be clearly seen that the heat transfer coefficient increases with the mass flux before ONB, but does not change obviously with equilibrium quality due to the dominant heat transfer mechanism of the forced convection. Meanwhile, the nucleate boiling starts at the negative equilibrium quality for all considered mass fluxes, and the equilibrium quality at ONB increases with the mass flux. Since the heat transfer coefficient increases with increasing the mass flux before ONB, the water temperature at ONB is proportional to the mass flux, and the equilibrium quality at ONB increases with the mass flux. Moreover, the heat transfer coefficient for different mass fluxes (Gl = 700 kg/m2 s, Gl = 1000 kg/m2 s, Gl = 1500 kg/m2 s) increases linearly and rapidly with equilibrium quality after ONB, and the discrepancy of heat transfer coefficient between different mass fluxes (Gl = 700 kg/m2 s, Gl = 1000 kg/m2 s, Gl = 1500 kg/ m2 s) decreases, which is attributed to the dominant heat transfer mechanism of the nucleate boiling. Once the nucleate boiling occurs (xe > xeONB), the bubbles rapidly generate and coalesce on the heating wall. Since the inner diameter of the mini-channel is obviously less than that of the conventional-channel, the velocity gradient along the radial direction is larger for the mini-channel. Thus, the shear force acting on the bubbles is more significant in the mini-channel, so the bubbles can easily depart from the heating wall. Also, the surface tension and the confinement of the mini-channel play important roles in the mini-channel, which cause the bubbles to quickly coalesce after departure from the heating wall. Therefore, the flow pattern rapidly transfers from the single phase to the slug flow after the nucleate boiling happening for different mass fluxes (Gl = 700 kg/m2 s, Gl = 1000 kg/m2 s, Gl = 1500 kg/m2 s), which is much different from the conventional-channel (Din = 6.88 mm). As for Gl = 700 kg/m2 s, the flow patterns for different equilibrium qualities are shown in Fig. 12. As shown in Fig. 12a, the flow pattern appears typical slug flow as xe = 0.0074, but the length of the vapor slug is small due to low heat flux. Meanwhile, the flow boiling fluctuation starts to appear for different mass fluxes (Gl = 700 kg/m2 s, Gl = 1000 kg/ m2 s, Gl = 1500 kg/m2 s) after ONB. As shown in Fig. 13a, the pressure drop for the specific working condition (Din = 2.15 mm, Tinlet = 80 °C, Gl = 700 kg/m2 s, xe = 0.0074) presents significant fluctuation of 13.29%, while the mass flux and the wall temperature at No. 7 remain stable. Therefore, the fully developed boiling (FDB) and quasi-stable boiling simultaneously appear once the

234

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

10

Δ P(kPa)

8 ΔPmean=6.08 kPa, Δ(ΔP)=9.25%

6

4

2 0

45

90 t (s)

135

180

135

310

125 Gl, mean=301.43 kg/m2s, ΔGl=0.67%

Twall, 7 (°C)

Gl (kg/m2s)

(1) Τhe fluctuation of pressure drop 320

300

Twall, 7, mean=112.66 °C, ΔTwall, 7=1.72%

115

105

290

95

280 0

45

90 t (s)

135

180

(2) The fluctuation of mass flux

0

45

90 t (s)

135

180

(3) The fluctuation of wall temperature

Fig. 7. The variation of experimental parameters with time (Din = 6.88 mm, Tinlet = 80 °C, Gl = 300 kg/m2 s, xe = 0.0034).

nucleate boiling occurs. As for xe > 0, the flow boiling accesses the saturated boiling region. As shown in Fig. 11, the heat transfer coefficient is mainly dependent on the mass flux rather than the equilibrium quality, but present obvious fluctuation with equilibrium quality, especially for Gl = 700 kg/m2 s. Moreover, the flow pattern appears to be slug flow instead of churn flow or annular flow, which is much different from the conventional-channel (Din = 6.88 mm). As shown in Fig. 12b, the flow pattern of Gl = 700 kg/m2 s still presents typical slug flow as xe = 0.0242, while the vapor slug length significantly increases and the liquid-vapor interface is more irregular compared to xe = 0.0074. Additionally, the fluctuation of pressure drop as xe = 0.0242 significantly enhances compared to xe = 0.0074, with the amplitude of 16.54% and the period of 94.65 s, as shown in Fig. 13b. Meanwhile, the mass flux and the wall temperature at No. 7 still remain stable, as shown in Fig. 13b. Since the bubbles generate, depart, and coalesce to the vapor slugs in the mini-channel, the channel is blocked and the pressure drop gradually increases. Since the vapor slug length is small, the flow resistance in the mini-channel is not significant and the period of vapor slug movement is short, which cause the characteristics of pressure drop as shown in Fig. 13a. With the equilibrium quality increasing, the vapor slug grows violently both in and opposite to the flow direction, and the elongated vapor slug is formed with long movement period. As the sufficient pressure drop is built-up, the elongated vapor slugs is rapidly

pushed out and the cyclic development of vapor slug is repeated. Therefore, the quasi-stable boiling in a single circular minichannel with the fluctuation of pressure drop is caused by the cyclic evolution of vapor slug. As the inlet water temperature decreases to 75 °C and 70 °C, the variation of heat transfer coefficient and wall superheat with equilibrium quality for different mass fluxes, and the boiling curves for different mass fluxes are illustrated in Fig. 14a and b, respectively. As shown in Figs. 11, 14a and 4b, it can be clearly seen that the heat transfer coefficient for different mass fluxes is not significantly affected by the inlet water temperatures in most respects. For example, the two-phase starts at the negative equilibrium quality for Tinlet = 75 °C and Tinlet = 70 °C, and the flow boiling mechanisms include the forced convection, the nucleate boiling, and the forced convection with evaporation. Also, the heat transfer coefficient increases with the mass flux, but changes little with equilibrium quality before ONB. Moreover, the quasi-stable boiling rapidly appears once the nucleate boiling occurs, and the intensity increases with the equilibrium quality. Meanwhile, the slug flow as the only flow pattern exists in the regions of the nucleate boiling and the forced convection with evaporation as Tinlet = 75 °C and Tinlet = 70 °C, which causes the unstable boiling due to the cyclic evolution of vapor slug. However, there are some differences for the flow boiling characteristics between different inlet water temperatures. Firstly, the wall superheat presents obvious undershoot

235

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

16 Single Phase Region Low Subcooled Region High Subcooled Region

r ce Fo

hwall, 7 (kW/m 2K )

12

8

FDB S

4

c ub

oo

le

d

N

u

te

on

v ec

tio

Boiling Crisis (Dryout)

quasi-stable boiling

ea cl

dC

ion rat ap o Ev ith w n Saturated Region

Bo

n ili

g

ONB

Forced

ction Conve

a

(0.0086) 0 -0.05 (-0.0313) -0.03 (-0.0204) -0.01(-0.0075) 0.01 xe7

0.03

xe=-0.0313

(1) hwall, 7-xe7

Isolated Bubbly Flow

b xe=-0.0204 Slug Flow

160

30 Single Phase Region

Low Subcooled Region High Subcooled Region

Saturated Region

15

130 Boiling Crisis (Dryout)

0

100 quasi-stable boiling

-15

Twater (°C)

Twall, 7-Tsat (°C)

quasi-stable boiling

70 ONB

FDB

Twall, 7-Tsat Twater

(0.0086)

-30 -0.05 (-0.0313) -0.03 (-0.0204) -0.01 (-0.0075) 0.01

40 0.03

xe7

c xe=-0.0075

(2) (Twall, 7-Tsat, 7)-xe7 300

Churn Flow

d xe=0.0086 Annular Flow

Fig. 9. The flow patterns with different equilibrium qualities (Din = 6.88 mm, Tinlet = 70 °C, Gl = 300 kg/m2 s).

Boiling Crisis (Dryout)

q (kW/m2)

225

quasi-stable boiling

150 FDB

ONB

75

0 -10

0

10 Twall, 7-Tsat (°C)

20

30

(3) q-(Twall, 7-Tsat, 7) Fig. 8. The flow boiling (Din = 6.88 mm, Tinlet = 70 °C, Gl = 300 kg/m2 s).

at ONB for different mass fluxes as Tinlet = 75 °C and Tinlet = 70 °C, except for the specific working condition (Tinlet = 75 °C, Gl = 700 kg/m2 s), where the wall superheat approaches a flat area to keep almost no change with equilibrium quality increasing, as shown

in Fig. 14a and b. As shown in Fig. 14a, the undershoots of wall superheats are 1.87 K and 1.93 K for Gl = 1000 kg/m2 s and Gl = 1500 kg/m2 s as Tinlet = 75 °C, respectively. As for Tinlet = 70 °C, the undershoot of wall superheat increases to 2.13 K for Gl = 1000 kg/m2 s, and present significant undershoot of 7.95 K for Gl = 700 kg/m2 s, as shown in Fig. 14b. Thus, it is concluded that the undershoot of wall superheat increases with decreasing the inlet water temperature. As shown in Fig. 14a, the equilibrium quality at ONB is proportional to the mass flux with Tinlet = 75 °C. However, it is inversely proportional with Tinlet = 70 °C, as shown in Fig. 14b. The further research is needed in future. As for current working conditions, the equilibrium quality at ONB for different mass fluxes does not present obvious regularity, and the heat transfer coefficient changes little with different inlet water temperatures. Moereover, the variation of heat transfer coefficient with equilibrium quality for conventional channel (Din = 6.88 mm) and mini channel (Din = 2.15 mm) with specific working conditions (Tin = 80 °C, Gl = 700 kg/m2 s) are shown in Fig. 15. Obviously, the nucleate boiling starts at negative equilibrium quality for both channels, but the equilibrium quality at ONB for conventional channel is smaller than that of mini channel due to larger cross-

236

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

10

8

Δ P(kPa)

ΔPmean=6.06 kPa, Δ(ΔP)=15.08%

6

4

2 0

45

90 t (s)

135

180

135

310

125

Twall, 7 (°C)

Gl (kg/m2s)

(1) The fluctuation of pressure drop 320

2 Gl, mean=297.00 kg/m s, ΔGl=0.22%

300

Twall, 7, mean =115.43 °C, ΔTwall, 7=1.21%

115

105

290

95

280 0

45

90 t (s)

135

0

180

45

90 t (s)

135

180

(3) The fluctuation of wall temperature

(2) The fluctuation of mass flux

Fig. 10. The variation of experimental parameters with time (Din = 6.88 mm, Tinlet = 70 °C, Gl = 300 kg/m2 s, xe = 0.0075).

sectional area for conventional channel. In addition, the characteristics of heat transfer mechanism evolution for conventional and mini channel are much different. The increasing of equilibrium quality is mild in conventional channel after ONB, but the equilibrium quality rapidly increases in mini channel once the vapor phase occurs. As for mini channel, vapor bubbles rapidly generate, depart and coalesce due to large shear force and surface tension as mentioned above. Meanwhile, the flow patterns rapidly transfer from single phase flow to slug flow. Thus, the dominated heat transfer mechanism quickly transfers from nucleate boiling to forced convection with evaporation. 4.3. Model for prediction of flow boiling heat transfer coefficients In this section, a modified correlation based on the Chen [28] correlation is proposed to predict the heat transfer coefficients for the flow boiling in channels with different inner diameter of 2.15 mm, 4.99 mm and 6.88 mm. In recent decades, the Chen [28] correlation was one of the most influential and most widely quoted correlations for the flow boiling heat transfer, which had been quoted over 1200 times as suggested by Chen and Fang [30]. In the research of Rohsenow [31], it was firstly proposed that the total heat transfer coefficient was composed of two components, including the forced convection mechanism and the pool boiling mechanism.

htp ¼ hfc þ hpb

ð13Þ

where htp is the heat transfer coefficient of the two-phase (kW/ m2 K); hfc is the heat transfer coefficient of the forced convection (kW/m2 K), and hpb is the heat transfer coefficient of the pool boiling (kW/m2 K). Chen [28] redeveloped a model based on the Rohsenow [31] correlation which was generally regarded as one of the best correlations for subcooled and saturated flow boiling.

htp ¼ Fhfc þ Shpb

ð14Þ

where hfc and hpb are calculated by the Dittus–Boelter [32] correlation and the Forster and Zuber [33] correlation, respectively. 0:4 hfc ¼ 0:023Re0:8 l Pr l

Rel ¼

Prl ¼

kl Din

Gl Din ð1  xe Þ

ll

ll C p;l

ð16Þ

ð17Þ

kl

hpb ¼ 0:00122

ð15Þ

q0:49 g 0:25 l 0:75 DT 0:24 sat DP sat 0:24 r0:5 l0:29 Hfg q0:24 g l 0:79 0:45 cp;l

kl

ð18Þ

237

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

32

hwall, 7 (kW/m2K)

24

ONB, FDB (Gl1500)

16

Nose

Middle Part

Tail

xe=-0.0074 (Slug Flow)

8

Gl700

Gl1000

ONB, FDB (Gl1000)

Gl1500

ONB, FDB (Gl700)

0 -0.050

-0.025

0.000 xe7

0.025

0.050

(1) hwall, 7-xe7 30 Nose

Twall, 7 -Tsat (°C)

15

Tail

xe=0.0242 (Slug Flow)

ONB, FDB (Gl1500 ) ONB, FDB (Gl1000 ) ONB, FDB (Gl700)

Fig. 12. The flow patterns with different equilibrium qualities. (Din = 2.15 mm, Tinlet = 80 °C, Gl = 700 kg/m2 s).

0

-15

Gl700

Gl1000 Gl1500

-30 -0.050

-0.025

0.000 xe7

0.025

0.050

(2) (Twall, 7-Tsat, 7)-xe7 400

300

2

q (kW/m )

Middle Part

ONB, FDB (Gl1500 )

200

ONB, FDB (Gl1000 ) ONB, FDB (Gl700)

100

Gl700

Gl1000 Gl1500 0 -30

-15

0 Twall, 7-Tsat (°C)

15

30

(3) q-(Twall, 7-Tsat, 7) Fig. 11. The flow boiling with different mass fluxes (Din = 2.15 mm, Tinlet = 80 °C).

where Rel is the Reynolds number of the liquid phase; Prl is the Prandtl number of the liquid phase; kl is the thermal conductivity of the liquid phase (W/m K); Din is the inner diameter of the channel (mm); cp,l is the specific heat of the liquid phase (J/kg K); ql and qg is the density of the liquid phase (kg/m3) and the vapor phase (kg/m3), respectively; ll is the dynamic viscosity of the liquid phase (N/sm2); r is the surface tension (N/m); Hfg is the latent heat of vaporization (J/kg); DTsat is the superheat of the heating wall (K), and DPsat (kPa) is the difference in vapor pressure corresponding to DTsat. In the Chen [28] correlation, the enhancement factor F and the suppression factor S are proposed, which accounting for the enhancement of the forced convection and the correlation of pool boiling overestimating the actual nucleate boiling, respectively. As for the saturated boiling, the value of F is always larger than unity, since the liquid velocity in two-phase flow is much higher than that in single-phase flow. Moreover, F is strictly a flow parameter and is the function of the Martinelli parameter Xtt. S (<1) reflects the fact that the effective superheat is smaller than that in pool boiling due to the thinner boundary layer. Also, S is assumed to be the function of the two-phase Reynolds number (Retp). As for the subcooled flow boiling, F is commonly set to unity due to no net vapor generation, the heat transfer coefficient of two-phase should be calculated as follows,

htp ¼ hfc þ Shpb

T w  T sat Tw  Tb

ð19Þ

where Tw is the wall temperature (°C); Tsat is the saturation temperature (°C), and Tb is the bulk temperature (°C). However, Chen [28] did not propose any parametric equations for F and S, which were determined empirically from experimental data. Since a graphical representation is inconvenient for application, authors have proposed lots of parametric equations of F and S. According to the research of Chen and Fang [30], it was found that some equations

238

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

32

12

8

Δ P(kPa)

Δ P(kPa)

ΔPmean=20.91 kPa, Δ(ΔP)=16.54%

26

10

ΔPmean=8.25 kPa, Δ(ΔP)=13.29%

20

14

6

8

4 0

45

90 t (s)

135

0

18 0

45

730

710

720

700

Gl (kg/m 2s)

Gl (kg/m2s)

135

180

(1) The fluctuation of pressure drop

(1) The fluctuation of pressure drop

Gl, mean=707.23 kg/m2s, ΔGl=0.42%

710

90 t (s)

690 2 Gl, mean=691.34 kg/m s, ΔGl=1.32%

680

700

670

690 0

45

90 t (s)

135

0

180

(2) The fluctuation of mass flux

90 t (s)

135

180

(2) The fluctuation of mass flux 125

125

115

Twall, 7 (°C)

115

Twall, 7 (°C)

45

Twall, 7, mean=105.70 °C, ΔTwall, 7=0.86%

105

Twall, 7, mean=105.70 °C, ΔTwall, 7=0.86%

105

95

95

85 0

45

90 t (s)

135

18 0

85 0

45

90 t (s)

135

(3) The fluctuation of wall temperature

(3) The fluctuation of wall temperature

a

b

180

Fig. 13. The variation of experimental parameters with time (Din = 2.15 mm, Tinlet = 80 °C, Gl = 700 kg/m2 s, a: xe = 0.0074; b: xe = 0.0242).

in the available literatures were not accurate, and some were mistyped in the original sources and then used by others. Additionally, they presented the available equations of F and S with the Chen

[28] graphical functions to provide a reference for correctly using the Chen [28] correlation. Therefore, the available equations of F and S are expressed as follows,

239

32

32

24

24

16

hwall, 7 (kW/m2K)

hwall, 7 (kW/m2K)

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

ONB, FDB (Gl1500)

8 ONB, FDB (Gl1000)

-0.025

ONB, FDB (Gl1000) ONB, FDB(Gl700)

8

Gl700

Gl700

Gl1000

ONB, FDB (Gl700)

0 -0.050

16

Gl1000

Gl1500

0.000 xe7

0.025

0 -0.050

0.050

-0.025

(1) hwall, 7-xe7

0.000 xe7

0.025

0.050

(1) hwall, 7-xe7 30

30

15 Twall, 7-Tsat (°C)

Twall, 7 -Tsat (°C)

15

ONB, FDB (Gl1500 ) ONB, FDB (Gl1000 ) ONB, FDB (G l700 )

0

ONB, FDB (Gl700) ONB, FDB (Gl1000)

0

-15

-15

G l700

Gl700

G l1000

Gl1000

G l1500

-30 -0.050

-0.025

0.000 xe7

0.025

-30 -0.050

0.050

(2) (Twall, 7-Tsat, 7)-xe7

0.000 xe7

0.025

0.050

(2) (Twall, 7-Tsat, 7)-xe7

400

400

300

300

ONB, FDB (Gl1500)

q (kW/m2)

q (kW/m2)

-0.025

ONB, FDB (Gl1000)

200

ONB, FDB (Gl700)

100

Gl700 Gl1000

-15

0 Twall, 7-Tsat (°C)

15

ONB, FDB (Gl700 )

100 Gl700

Gl1000

Gl1500

0 -30

ONB, FDB (Gl1000 )

200

0 -30

30

-15

0 Twall, 7 -Tsat (°C)

15

(3) q-(Twall, 7-Tsat, 7)

(3) q-(Twall, 7-Tsat, 7)

a

b

30

Fig. 14. The flow boiling with different mass fluxes (a: Din = 2.15 mm, Tinlet = 75 °C; b: Din = 2.15 mm, Tinlet = 70 °C).

F ¼ 2:35ð1=X tt þ 0:213Þ0:736 F ¼ 1 ð1=X tt 6 0:1Þ

ð1=Xtt > 0:1Þ

ð20Þ ð21Þ

X tt ¼

 0:9  0:5  0:1 1  xe qv ll xe ql lv

ð22Þ

240

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

32

S¼

hwall, 7 (W/m2K)

htp ¼

FDB (Din7Tinlet80) ONB (Din7Tinlet80)

Din2Tinlet80

-0.025

0.000 xe7

0.025

0.050

Fig. 15. The variation of heat transfer coefficient with equilibrium quality for different channels (Gl = 700 kg/m2 s).

1 1 þ 2:53  106 ðRel F 1:25 Þ

1:17

i

ð23Þ

Gungor and Winterton [34] proposed that the enhancement factor F was not just dependent on the Martinelli parameter Xtt and was significantly affected by the generation of vapor. Thus, the enhancement factor F was the function of the Martinelli parameter Xtt and the boiling number Bo.

F ¼ 1 þ 2:4  104 Bo1:16 þ 1:37ð1=X tt Þ0:86 q Hfg Gl

ð24Þ ð25Þ

2

2

where q is the heat flux (kW/m ), and Gl is the mass flux (kg/m s). Also, the suppression factor S is dominated by the two-phase Reynolds number, hence S is expressed as follows,

S¼

1 6 2

1 þ 1:15  10 F

Re1:17 l

ð26Þ

The heat transfer coefficient of the pool boiling hpb is calculated by Cooper [35] correlation, which is different from the Chen [28] correlation.

hpb

 0:12   0:55 P P ¼ 55 log10 M0:5 q0:67 Pcr Pcr

ð27Þ

where M is the molecular weight; P is the pressure (kPa), and Pcr is the critical pressure (kPa). Also, the heat transfer coefficient of twophase flow for the saturated boiling is expressed as Eq. (14). In the case of subcooled boiling, the driving temperature differences for the forced convection and the nucleate boiling are different, so the heat transfer coefficient of two-phase flow is expressed as Eq. (19). In the study of Liu and Winterton [36], it was suggested that the boiling number Bo contained in the forced convection term was not applicable in the case of subcooled boiling, and the Prandtl number Pr was used to modify the enhancement factor F.

  0:35 ql F ¼ 1 þ xe Pr l 1

qv

ð30Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 T w  T sat 2 htp ¼ ðFhfc Þ þ Shpb Tw  Tb

Din7Tinlet70

ONB, FDB (Din2Tinlet80)

0 -0.050

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðFhfc Þ þ ðShpb Þ

This expression than the simple addition has an advantage that the nucleate boiling can be further suppressed once the forced convection term is significantly larger than the pool boiling term. Therefore, the correlation of heat transfer coefficient of two-phase during the subcooled boiling is expressed as follow,

16

8

Bo ¼

ð29Þ

Meanwhile, a modified expression based on the power-type addition model was proposed by Kutateladze [37] as follows,

24

S¼h

1 1 þ 0:055F 0:1 Re0:16 l

ð28Þ

Moreover, the suppression factor S was controlled by the intensity of the forced convection mechanism, which could be calculated as follows,

ð31Þ

All the correlations for the flow boiling heat transfer coefficients mentioned above are listed in Table 2. The experimental results of flow boiling heat transfer coefficients obtained in this experimental study are compared with the Chen [28] correlation, the correlation proposed by Gungor and Winterton [34], and the correlation proposed by Liu and Winterton [36], respectively, as shown in Fig. 16a to c. It can be clearly seen that all the predicted values are overestimated compared to the experimental values. According to analysis, it is found that the enhancement factor F proposed in these correlations is too strong and the suppression factor S is too weak, which cause the predicted values to be much larger than the experimental values. Moreover, all the correlations mentioned above do not consider the effect of channel diameter, which has significant influence on the flow boiling heat transfer as discussed in Sections 4.1 and 4.2. Therefore, a modified model based on the Chen correlation is proposed as follows,

htp ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðFhfc Þ þ ðShpb Þ ðsaturated boilingÞ

ð32Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 T w  T sat 2 ðsubcooled boilingÞ htp ¼ ðFhfc Þ þ Shpb Tw  Tb 0:4 hfc ¼ 0:023Re0:8 l Pr l

hpb ¼ 0:00122

kl Din

0:79 0:45 cp;l

kl

r l 0:5

ð34Þ

q

0:49 0:25 g l 0:29 0:24 0:24 H g fg l

q

0:75 DT 0:24 sat DP sat

ð35Þ

F ¼ 1 þ 2:4  104 Bo1:26 þ 0:87ð1=X tt Þ0:32 S¼h

1 6

1 þ 2:53  10 ðRel F

ð33Þ

1:25 1:14

Þ

þ 1:75ðNconf Þ0:3

ð36Þ i

ð37Þ

As for this newly developed correlation, the confinement number (Nconf) is proposed in suppression factors S to reflect the effect of channel diameter on flow boiling heat transfer, which means the ratio of vapor bubble departure diameter and channel diameter. With decreasing the channel diameter, the confinement number (Nconf) increases and suppression factor S decreases. It is favorable for vapor bubbles to coalesce and the lengths of vapor slugs rapidly increases, which cause the nucleate boiling to be restrained. To validate the accuracy of this model, a comparison between the and experimental results is carried out. Those experimental results are obtained under a wide range of working conditions including

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

241

Table 2 Empirical correlations for the flow boiling heat transfer coefficients. Number

Reference

Empirical Correlation

Applicable Ranges

1

Chen [28]

htp ¼ Fhfc þ Shpb (saturated boiling),

Deionized water, methanol, cyclohexane, pentane;

sat htp ¼ hfc þ Shpb TTwwT T b (subcooled boiling)

0:4 kl hfc ¼ 0:023Re0:8 l Pr l Din , Rel ¼

Pr l ¼

ll C p;l

ql v l Din ð1xe Þ , ll

Saturated flow; Convective flow; Vertical and axial flow; Stable flow; No slug flow; No liquid deficiency; Heat flux less than critical flux;

kl 0:79 0:45

kl

c

q0:49 g0:25

0:24 0:75 p;l l hpb ¼ 0:00122 r0:5 l0:29 0:24 DT sat DP sat , H0:24 fg qg l  0:9  0:5  0:1 qv ll e X tt ¼ 1x xe q l v

l

F ¼ 2:35ð1=X tt þ 0:213Þ0:736 ð1=X tt > 0:1Þ, 1

F ¼ 1 ð1=X tt < 0:1Þ; S ¼ 6 1:25 1:17 1þ2:5310

2

Gungor and Winterton [34]

ðRel F

Þ

htp ¼ Fhfc þ Shpb (saturated boiling), sat htp ¼ hfc þ Shpb TTwwT T b (subcooled boiling)

0:4 kl hfc ¼ 0:023Re0:8 l Pr l Din ,  0:12 h  i0:55 P hpb ¼ 55 Pcr log10 PPcr M 0:5 q0:67 ,

Deionized water, refrigerant, ethylene and glycol; Din = 2.95 mm-32.00 mm; Vertical up/down channel, Horizontal channel, Annular channel; Saturated /Subcooled boiling; Psystem: 1 bar-202.60 bar;

Bo ¼ HfgqGl

3

Liu and Winterton [36]

F ¼ 1 þ 2:4  104 Bo1:16 þ 1:37ð1=X tt Þ0:86 , 1 S¼ 1þ1:15106 F 2 Re1:17 l qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 htp ¼ ðFhfc Þ þ ðShpb Þ (saturated boiling), rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi htp ¼

sat ðFhfc Þ þ Shpb TTwwT T b

2

2

Deionized water, refrigerant, ethylene and glycol; Din = 2.95 mm-32.00 mm; Vertical up/down channel, Horizontal channel, Annular channel; Saturated/Subcooled boiling; Psystem: 1 bar-202.60 bar;

kl (subcooled boiling), hfc ¼ 0:023Rel0:8 Pr 0:4 l Din ,   0:35 ql F ¼ 1 þ xe Prl q  1 v  0:12 h  i0:55 hpb ¼ 55 PPcr log10 PPcr M 0:5 q0:67 ,

4

Modified correlation in present study

S ¼ 1þ0:055F1 0:1 Re0:16 l qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 htp ¼ ðFhfc Þ þ ðShpb Þ (saturated boiling), rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2ffi 2 sat htp ¼ ðFhfc Þ þ Shpb TTwwT T b

Deionized water; Din = 2.15 mm,4.99 mm, 6.88 mm; Vertical up channel; Saturated/ Subcooled boiling;

kl (subcooled boiling), hfc ¼ 0:023Rel0:8 Pr 0:4 l Din ,

F ¼ 1 þ 2:4  104 Bo1:26 þ 0:87ð1=X tt Þ0:32 0:79 0:45

kl

c

q0:49 g0:25

0:75 p;l l hpb ¼ 0:00122 r0:5 l0:29 DT 0:24 sat DP sat , H0:24 q0:24 l

S¼

fg

g

1

1:14 1þ2:53106 ðRel F 1:25 Þ þ1:75ðN conf Þ0:3

different channel diameters, inlet water temperatures, mass fluxes and heat fluxes. As shown in Fig. 16d, a good agreement is achieved with all the errors less than ±30% and most of them less than ±20%. 5. Conclusions An experimental study is carried out to investigate the flow boiling heat transfer in channels with different inner diameters of 2.15 mm, 4.99 mm, and 6.88 mm. The conclusions are obtained as follows: (1) The channel with inner diameter of 2.15 mm presents typical ‘‘mini-channel characteristics” in the flow boiling heat transfer, which is different from that of conventionalchannel (Din = 6.88 mm). Both mechanisms of the nucleate boiling and the forced convection with evaporation dominate in the conventional-channel (Din = 6.88 mm) and mini-channel (Din = 2.15 mm) under different working conditions. (2) As for conventional-channel (Din = 6.88 mm), the equilibrium quality of ONB is not significantly affected by the mass flux for Tinlet = 80 °C and Tinlet = 70 °C. The thermal equilibrium qualities at ONB and FDB for Tinlet = 80 °C are significantly larger than those for Tinlet = 70 °C. As for

mini-channel (Din = 2.15 mm), the undershoot of wall superheat at ONB increases with the inlet water temperature decreasing, and the equilibrium quality at ONB is proportional to the mass flux for Tinlet = 80 °C and Tinlet = 75 °C, except for Tinlet = 70 °C. While, the equilibrium quality at ONB for specific mass flux does not present obvious regularity, and the heat transfer coefficient for specific mass flux changes little with the inlet water temperature varying. FDB and the quasi-stable boiling simultaneously appear once the nucleate boiling happens, and the slug flow as the only flow pattern exists in the regions of the nucleate boiling and the forced convection with evaporation. Additionally, the quasi-stable boiling in a single circular mini-channel is caused by the cyclic evolution of vapor slug. (3) A modified correlation based on the Chen [28] correlation is proposed to predict the flow boiling heat transfer coefficients in the large-channel and mini-channel. In this model, the effects of the channel confinement (Nconf), vapor generation (Bo), and interaction between two phases (Xtt) are taken into account. According to the comparison between the predicted and experimental results under a wide range working conditions, a good agreement is achieved with an uncertainty less than ±30%.

242

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243

100

100

80

+20%

80

+20%

+30%

+30% -20% htp, pre (kW/m 2K)

htp, pre (kW/m 2K)

-20% 60

-30%

40

MRE=92.20% Din=2.15 mm

20

60

-30%

40

MRE=39.21% Din=2.15 mm

20

Din=4.99 mm

Din=4.99 mm

Din=6.88 mm

Din=6.88 mm

0

0 0

20

40

60

80

0

10 0

20

40

60

80

Gungor and Winterton [34]

Chen [28] correlation 50

100

80

+30%

+20%

+30%

40

+20% -20%

60

2

2

htp, pre (kW/m K)

-20% htp, pre (kW/m K)

10 0

htp, exp (kW/m 2K)

htp, exp (kW/m 2K)

-30%

40

MRE=37.64% Din=2.15 mm

20

30

-30%

20

MRE=14.07% Din=2.15 mm

10

Din=4.99 mm

Din=4.99 mm

Din=6.88 mm

Din=6.88 mm

0

0 0

20

40 60 htp, exp (kW/m2K)

80

100

Liu and Winterton [36]

0

10

20 30 htp, exp (kW/m2K)

40

50

Present study

Fig. 16. The comparisons between the predicted and experimental results based on the typical models proposed in literature and the model in present study.

Acknowledgement The authors are grateful for the support of the National Natural Science Foundation of China (No. 51206199), and the project funded by China Postdoctoral Science Foundation (No. 2014M562337).

References [1] S.G. Kandlikar, Fundamental issues related to flow boiling in minichannels and microchannels, Exp. Thermal Fluid Sci. 26 (2–4) (2002) 389–407. [2] S.S. Mehendale, A.M. Jacobi, R.K. Shah, Fluid flow and heat transfer at microand meso-scales with application to heat exchanger design, Appl. Mech. Rev. 53 (7) (2000) 175–193. [3] L. Chen, Y.S. Tian, T.G. Karayiannis, The effect of tube diameter on vertical twophase flow regimes in small tubes, Int. J. Heat Mass Transfer 49 (21–22) (2006) 4220–4230. [4] G. Ribatski, L. Wojtan, J.R. Thome, An analysis of experimental data and prediction methods for two-phase frictional pressure drop and flow boiling heat transfer in micro-scale channels, Exp. Thermal Fluid Sci. 31 (1) (2006) 1– 19. [5] P.A. Kew, K. Cornwell, Correlations for the prediction of boiling heat transfer in small-diameter channels, Appl. Therm. Eng. 17 (8–10) (1997) 705–715. [6] R. Charnay, R. Revellin, J. Bonjour, Flow boiling heat transfer in minichannels at high saturation temperatures: Part I – experimental investigation and analysis of the heat transfer mechanisms, Int. J. Heat Mass Transfer 87 (2015) 636–652.

[7] T.N. Tran, M.W. Wambsganss, D.M. France, Small circular- and rectangularchannel boiling with two refrigerants, Int. J. Multiph. Flow 22 (3) (1996) 485– 498. [8] C. Vlasie, H. Macchi, J. Guilpart, B. Agostini, Flow boiling in small diameter channels, Int. J. Refrig. 27 (2) (2004) 191–201. [9] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, Clarendon Press, 1996. [10] Z.Y. Bao, D.F. Fletcher, B.S. Haynes, Flow boiling heat transfer of Freon R11 and HCFC123 in narrow passages, Int. J. Heat Mass Transfer 43 (18) (2000) 3347– 3358. [11] R. Ali, B. Palm, M.H. Maqbool, Flow boiling heat transfer characteristics of a minichannel up to dryout condition, J. Heat Transfer 133 (8) (2011), 081501081501. [12] X. Huo, L. Chen, Y.S. Tian, T.G. Karayiannis, Flow boiling and flow regimes in small diameter tubes, Appl. Therm. Eng. 24 (8–9) (2004) 1225–1239. [13] S. Lin, P.A. Kew, K. Cornwell, Flow boiling of refrigerant R141B in small tubes, Chem. Eng. Res. Des. 79 (4) (2001) 417–424. [14] W. Qu, I. Mudawar, Flow boiling heat transfer in two-phase micro-channel heat sinks––I. Experimental investigation and assessment of correlation methods, International, J Heat Mass Transfer 46 (15) (2003) 2755–2771. [15] K.H. Bang, K.K. Kim, S.K. Lee, B.W. Lee, Pressure effect on flow boiling heat transfer of water in minichannels, Int. J. Therm. Sci. 50 (3) (2011) 280–286. [16] T.G. Karayiannis, M.M. Mahmoud, D.B.R. Kenning, A study of discrepancies in flow boiling results in small to microdiameter metallic tubes, Exp. Thermal Fluid Sci. 36 (2012) 126–142. [17] B. Sumith, F. Kaminaga, K. Matsumura, Saturated flow boiling of water in a vertical small diameter tube, Exp. Thermal Fluid Sci. 27 (7) (2003) 789–801. [18] M. Piasecka, M.E. Poniewski, Hysteresis phenomena at the onset of subcooled nucleate flow boiling in microchannels, Heat Transfer Eng. 25 (3) (2004) 44– 51.

Q. Lu et al. / International Journal of Heat and Mass Transfer 107 (2017) 225–243 [19] Y.M. Lie, T.F. Lin, Subcooled flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct, Int. J. Heat Mass Transfer 49 (13–14) (2006) 2077–2089. [20] Z. Liu, Q. Bi, Onset and departure of flow boiling heat transfer characteristics of cyclohexane in a horizontal minichannel, Int. J. Heat Mass Transfer 88 (2015) 398–405. [21] W. Owhaib, C. Martı´n-Callizo, B. Palm, Evaporative heat transfer in vertical circular microchannels, Appl. Therm. Eng. 24 (8–9) (2004) 1241–1253. [22] S. Saitoh, H. Daiguji, E. Hihara, Effect of tube diameter on boiling heat transfer of R-134a in horizontal small-diameter tubes, Int. J. Heat Mass Transfer 48 (23–24) (2005) 4973–4984. [23] E. Sobierska, R. Kulenovic, R. Mertz, Heat transfer mechanism and flow pattern during flow boiling of water in a vertical narrow channel—experimental results, Int. J. Therm. Sci. 46 (11) (2007) 1172–1181. [24] V. Dupont, J.R. Thome, Evaporation in microchannels: influence of the channel diameter on heat transfer, Microfluid. Nanofluid. 1 (2) (2004) 119–127. [25] L. Consolini, J.R. Thome, Micro-channel flow boiling heat transfer of R134a, R236fa, and R245fa, Microfluid. Nanofluid. 6 (6) (2009) 731–746. [26] H. Ohta, K. Inoue, M. Ando, K. Watanabe, Experimental Investigation on observed scattering in heat transfer characteristics for flow boiling in a small diameter tube, Heat Transfer Eng. 30 (1–2) (2009) 19–27. [27] D. Brutin, F. Topin, L. Tadrist, Experimental study of unsteady convective boiling in heated minichannels, Int. J. Heat Mass Transfer 46 (16) (2003) 2957– 2965.

243

[28] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Ind. Eng. Chem. Process Des. Dev. 5 (3) (1966) 322–329. [29] L.S. Tong, Y.S. Tang, Boiling Heat Transfer and Two-Phase Flow, Taylor & Francis, Washington, D.C., 1997. [30] W. Chen, X. Fang, A note on the Chen correlation of saturated flow boiling heat transfer, Int. J. Refrig. 48 (2014) 100–104. [31] W.M. Rohsenow, Chapter in Heat Transfer, University of Michigan Press, Ann Arbor, IL, 1953. [32] F.W. Dittus, L.M.K. Boelter, Heat transfer in automobile radiators of the tubular type, Univ. California Publ. Eng. 2 (1930) 443–461. [33] H.K. Forster, N. Zuber, Dynamics of vapor bubbles and boiling heat transfer, IChE J. 1 (4) (1955) 531–535. [34] K.E. Gungor, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transfer 29 (3) (1986) 351–358. [35] M.G. Cooper, Saturation nucleate pool boiling, a simple correlation, in: First U. K. National Conference on Heat Transfer, 1984. [36] Z. Liu, R.H.S. Winterton, A general correlation for saturated and subcooled flow boiling in tubes and annuli, based on a nucleate pool boiling equation, Int. J. Heat Mass Transfer 34 (11) (1991) 2759–2766. [37] S.S. Kutateladze, Boiling heat transfer, Int. J. Heat Mass Transfer 4 (1961) 31– 45.